Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#20263346 | C2 | semidirect |
| 2. #27161646 | C2 | semidirect |
| 3. #27161562 | C2 | semidirect |
| 4. #27161299 | C2 | semidirect |
| 5. #27161292 | C2 | semidirect |
| 6. #27161277 | C2 | semidirect |
| 7. #27161272 | C2 | semidirect |
| 8. #27161107 | C2 | semidirect |
| 9. #27161081 | C2 | semidirect |
| 10. C2×#20263247 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C197 | C2 | semidirect |
| 14. C2×#15691348 | C22 | semidirect |
| 15. C2×#15691346 | C22 | semidirect |
| 16. C2×#15691345 | C22 | semidirect |
| 17. C2×#15691343 | C22 | semidirect |
| 24. Q8×Dic197 | C22 | semidirect |
| 26. D4×Dic197 | C22 | semidirect |
| 31. #20263255 | C22 | semidirect |
| 32. #20263255 | C22 | semidirect |
| 33. #20263251 | C22 | semidirect |
| 34. #20263248 | C22 | semidirect |
| 73. #41×C197 | D4 | semidirect |
| 154. C197 | #3045 | semidirect |
| 156. C2×AGL(1,ℤ/8) | D197 | semidirect |
| 202. #41 | C22⋊D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263346 | 2 |
| #27161646 | 2 |
| #27161562 | 2 |
| #27161299 | 2 |
| #27161292 | 2 |
| #27161277 | 2 |
| #27161272 | 2 |
| #27161107 | 2 |
| #27161081 | 2 |
| C2×#20263247 | 2 |
| C2×AGL(1,ℤ/8)×C197 | 2 |
| #3045 | 197 |